Mapping Node, Box projection, and rotation
"I'm trying to map a texture to a cube"


Perhaps a simpler way of mapping a texture to a cube and have control of the orientation of the texture on each of the 6 faces is to use UV mapping?

Starting with the node setup you have already :


In the Texture Coordinate node change to UV, and the Mapping node change to Point (and reset the rotation and scale to Zero).
Drag open a new viewport and change Editor Type to UV Editor.
3D viewport > Edit Mode > select the cube, then U to open the UV Mapping menu and choose the Reset option. This will reset the UV's so that each face of the cube is mapped to the complete UV space. (Each face stacked one above the other).
3D Viewport > select the face that you would like to change the orientation of the texture.
In the UV Viewport > select the face (if it is not already highlighted in orange then use the A key to select it) and rotate it 90° with R90.




Or you can probably find the answer here http://www.blenderinsight.com/beginners-guide-to-cycles-nodes-the-procedural-way/  Under the chapter titled Object (with no reference object) :)